Probability Theory and Related Fields, ISSN 0178-8051, 8/2016, Volume 165, Issue 3, pp. 559 - 580

We provide a short proof of the Ray-Knight second generalized Theorem, using a martingale which can be seen (on the positive quadrant) as the Radon–Nikodym...

81T25 | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Primary 60J27 | Probability Theory and Stochastic Processes | 81T60 | Mathematics | Operation Research/Decision Theory | Secondary 60K35 | Quantitative Finance | 60J55 | THEOREM | STATISTICS & PROBABILITY | REINFORCED JUMP-PROCESSES | Markov processes | Studies | Probability | Markov analysis | Mathematical analysis | Quadrants | Theorems | Theorem proving | Probability theory | Inversions | Derivatives | Martingales

81T25 | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Primary 60J27 | Probability Theory and Stochastic Processes | 81T60 | Mathematics | Operation Research/Decision Theory | Secondary 60K35 | Quantitative Finance | 60J55 | THEOREM | STATISTICS & PROBABILITY | REINFORCED JUMP-PROCESSES | Markov processes | Studies | Probability | Markov analysis | Mathematical analysis | Quadrants | Theorems | Theorem proving | Probability theory | Inversions | Derivatives | Martingales

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 2/2010, Volume 91, Issue 2, pp. 167 - 197

We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov...

Geometry | Theoretical, Mathematical and Computational Physics | gauge theory | 81T60 | conformal field theory | Group Theory and Generalizations | 81T40 | Statistical Physics, Dynamical Systems and Complexity | Physics | Conformal field theory | Gauge theory | SYMMETRY | PHYSICS, MATHEMATICAL | VERTEX | Physics - High Energy Physics - Theory

Geometry | Theoretical, Mathematical and Computational Physics | gauge theory | 81T60 | conformal field theory | Group Theory and Generalizations | 81T40 | Statistical Physics, Dynamical Systems and Complexity | Physics | Conformal field theory | Gauge theory | SYMMETRY | PHYSICS, MATHEMATICAL | VERTEX | Physics - High Energy Physics - Theory

Journal Article

Advances in Theoretical and Mathematical Physics, ISSN 1095-0761, 2004, Volume 8, Issue 6, pp. 987 - 1000

We show that for every positive curvature Kahler Einstein manifold in dimension 2n there is a countably infinite class of associated Sasaki Einstein manifolds...

PHYSICS, MATHEMATICAL | METRICS | PHYSICS, PARTICLES & FIELDS | 81T60 | 53C25

PHYSICS, MATHEMATICAL | METRICS | PHYSICS, PARTICLES & FIELDS | 81T60 | 53C25

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 4/2019, Volume 173, Issue 3, pp. 1349 - 1387

In this paper, we define an extension of the supersymmetric hyperbolic nonlinear sigma model introduced by Zirnbauer. We show that it arises as a weak joint...

Secondary 81T60 | Vertex-reinforced jump process | Statistics for Business, Management, Economics, Finance, Insurance | Primary 60K35 | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Self-interacting random walks | Probability Theory and Stochastic Processes | Mathematics | Supersymmetric hyperbolic nonlinear sigma model | Quantitative Finance | STATISTICS & PROBABILITY | Analysis | Resveratrol | Variations | Supersymmetry | Field theory | Nonlinear systems | Probability

Secondary 81T60 | Vertex-reinforced jump process | Statistics for Business, Management, Economics, Finance, Insurance | Primary 60K35 | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Self-interacting random walks | Probability Theory and Stochastic Processes | Mathematics | Supersymmetric hyperbolic nonlinear sigma model | Quantitative Finance | STATISTICS & PROBABILITY | Analysis | Resveratrol | Variations | Supersymmetry | Field theory | Nonlinear systems | Probability

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 10/2015, Volume 339, Issue 1, pp. 121 - 148

We show transience of the edge-reinforced random walk (ERRW) for small reinforcement in dimension $${d\ge3}$$ d ≥ 3 . This proves the existence of a phase...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | LOCALIZATION | JUMP-PROCESSES | TREES | PHYSICS, MATHEMATICAL | GRAPHS | Probability | Mathematics

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | LOCALIZATION | JUMP-PROCESSES | TREES | PHYSICS, MATHEMATICAL | GRAPHS | Probability | Mathematics

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 6/2019, Volume 109, Issue 6, pp. 1377 - 1395

We discuss supersymmetric surface defects in compactifications of six-dimensional minimal conformal matter of types SU(3) and SO(8) to four dimensions. The...

Geometry | Integrable models | Theoretical, Mathematical and Computational Physics | Complex Systems | 81T99 | 81T60 | Group Theory and Generalizations | Duality | Supersymmetric theories | Physics

Geometry | Integrable models | Theoretical, Mathematical and Computational Physics | Complex Systems | 81T99 | 81T60 | Group Theory and Generalizations | Duality | Supersymmetric theories | Physics

Journal Article

Journal of the American Mathematical Society, ISSN 0894-0347, 04/2019, Volume 32, Issue 2, p. 311

This paper concerns the vertex reinforced jump process (VRJP), the edge reinforced random walk (ERRW), and their relation to a random Schrödinger operator. On...

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 12/2011, Volume 98, Issue 3, pp. 225 - 287

To every 3-manifold M one can associate a two-dimensional $${\mathcal{N}=(2, 2)}$$ supersymmetric field theory by compactifying five-dimensional...

D-branes | Theoretical, Mathematical and Computational Physics | 14N35 | vortex equations | conformal field theory | Statistical Physics, Dynamical Systems and Complexity | Physics | Geometry | 81T30 | BPS invariants | gauge theory | 81T60 | Group Theory and Generalizations | 81T40 | GAUGE-THEORY | FLAG MANIFOLDS | BRANES | PHYSICS, MATHEMATICAL

D-branes | Theoretical, Mathematical and Computational Physics | 14N35 | vortex equations | conformal field theory | Statistical Physics, Dynamical Systems and Complexity | Physics | Geometry | 81T30 | BPS invariants | gauge theory | 81T60 | Group Theory and Generalizations | 81T40 | GAUGE-THEORY | FLAG MANIFOLDS | BRANES | PHYSICS, MATHEMATICAL

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 3/2010, Volume 91, Issue 3, pp. 265 - 287

Using the thermodynamic Bethe ansatz method we derive an infinite set of integral non-linear equations for the spectrum of states/operators in AdS/CFT. The...

Geometry | 81T13 | 81T30 | integrability | 81T20 | gauge/string duality | Theoretical, Mathematical and Computational Physics | 81T60 | Group Theory and Generalizations | finite volume spectrum | Statistical Physics, Dynamical Systems and Complexity | Physics | Gauge/string duality | Integrability | Finite volume spectrum | EQUATIONS | PHYSICS, MATHEMATICAL | GORDON | BETHE-ANSATZ | Thermodynamics | High Energy Physics - Theory

Geometry | 81T13 | 81T30 | integrability | 81T20 | gauge/string duality | Theoretical, Mathematical and Computational Physics | 81T60 | Group Theory and Generalizations | finite volume spectrum | Statistical Physics, Dynamical Systems and Complexity | Physics | Gauge/string duality | Integrability | Finite volume spectrum | EQUATIONS | PHYSICS, MATHEMATICAL | GORDON | BETHE-ANSATZ | Thermodynamics | High Energy Physics - Theory

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2015, Volume 17, Issue 9, pp. 2353 - 2378

Edge-reinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986 [8], is a random process which takes values in the vertex set of a graph G...

Reinforcement | Self-interacting random walk | Supersymmetry | De Finetti theorem | Random walk in random environment | Sigma models | supersymmetry | LOCALIZATION | MATHEMATICS, APPLIED | ENVIRONMENT | de Finetti theorem | sigma models | random walk in random environment | BAYESIAN-ANALYSIS | GRAPHS | MATHEMATICS | TREES | LIMIT-THEOREMS | REVERSIBLE MARKOV-CHAINS | ATTRACTING EDGE | RECURRENCE | reinforcement

Reinforcement | Self-interacting random walk | Supersymmetry | De Finetti theorem | Random walk in random environment | Sigma models | supersymmetry | LOCALIZATION | MATHEMATICS, APPLIED | ENVIRONMENT | de Finetti theorem | sigma models | random walk in random environment | BAYESIAN-ANALYSIS | GRAPHS | MATHEMATICS | TREES | LIMIT-THEOREMS | REVERSIBLE MARKOV-CHAINS | ATTRACTING EDGE | RECURRENCE | reinforcement

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 10/2013, Volume 2013, Issue 10, p. 1

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) Abstract The off-shell representation theory of 4D, ... = 1 supermultiplets can...

Extended supersymmetry | Superspaces | Supergravity models

Extended supersymmetry | Superspaces | Supergravity models

Journal Article

Selecta Mathematica, ISSN 1022-1824, 12/2019, Volume 25, Issue 5, pp. 1 - 50

We consider a cluster variety associated to a triangulated surface without punctures. The algebra of regular functions on this cluster variety possesses a...

Mathematics, general | 81T60 | Mathematics | 13F60 | 16G20 | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | SKEIN | SURFACE | DUALITY | CLUSTER ALGEBRAS | VARIABLES | POTENTIALS | QUIVER GRASSMANNIANS | MODULI | GEOMETRY

Mathematics, general | 81T60 | Mathematics | 13F60 | 16G20 | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | SKEIN | SURFACE | DUALITY | CLUSTER ALGEBRAS | VARIABLES | POTENTIALS | QUIVER GRASSMANNIANS | MODULI | GEOMETRY

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 10/2011, Volume 98, Issue 1, pp. 33 - 64

In their recent paper, Alday et al. (Lett Math Phys 91:167–197, 2010) proposed a relation between $${\mathcal{N}=2}$$ four-dimensional supersymmetric gauge...

Geometry | Theoretical, Mathematical and Computational Physics | gauge theory | 81T60 | conformal field theory | Group Theory and Generalizations | 81T40 | Statistical Physics, Dynamical Systems and Complexity | Physics | WAVES | SYMMETRY | Q-OPERATOR | FIELD-THEORY | ALGEBRA | REPRESENTATION | MULTIPOINT CORRELATION-FUNCTIONS | PHYSICS, MATHEMATICAL | INTEGRABLE STRUCTURE | Mathematics | Mathematical Physics | High Energy Physics - Theory

Geometry | Theoretical, Mathematical and Computational Physics | gauge theory | 81T60 | conformal field theory | Group Theory and Generalizations | 81T40 | Statistical Physics, Dynamical Systems and Complexity | Physics | WAVES | SYMMETRY | Q-OPERATOR | FIELD-THEORY | ALGEBRA | REPRESENTATION | MULTIPOINT CORRELATION-FUNCTIONS | PHYSICS, MATHEMATICAL | INTEGRABLE STRUCTURE | Mathematics | Mathematical Physics | High Energy Physics - Theory

Journal Article

Advances in Theoretical and Mathematical Physics, ISSN 1095-0761, 2011, Volume 15, Issue 6, pp. 1909 - 1970

Adinkras are diagrams that describe many useful supermultiplets in D = 1 dimensions. We show that the topology of the Adinkra is uniquely determined by a...

PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 11/2017, Volume 107, Issue 11, pp. 2147 - 2187

We define an elliptic deformation of the Virasoro algebra. We conjecture that the $$\mathbb {R}^4\times \mathbb {T}^2$$ R 4 × T 2 Nekrasov partition function...

Elliptic Virasoro algebra | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | AGT | Geometry | Supersymmetric gauge theories | 17B68 | 81R10 | 81T20 | 81R50 | 81T60 | Group Theory and Generalizations | 81T40 | MATRIX DESCRIPTION | STRINGS | GAUGE-THEORIES | ALGEBRAS | VERTEX | DUALITY | BRANES | GENERA | PHYSICS, MATHEMATICAL | Astronomy | Algebra | Fysik | Physical Sciences | Naturvetenskap | Natural Sciences

Elliptic Virasoro algebra | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | AGT | Geometry | Supersymmetric gauge theories | 17B68 | 81R10 | 81T20 | 81R50 | 81T60 | Group Theory and Generalizations | 81T40 | MATRIX DESCRIPTION | STRINGS | GAUGE-THEORIES | ALGEBRAS | VERTEX | DUALITY | BRANES | GENERA | PHYSICS, MATHEMATICAL | Astronomy | Algebra | Fysik | Physical Sciences | Naturvetenskap | Natural Sciences

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 1/2017, Volume 107, Issue 1, pp. 1 - 30

We explore a new connection between Seiberg–Witten theory and quantum statistical systems by relating the dual partition function of SU(2) Super Yang–Mills...

70S15 | Fermi gas | 82D05 | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Quantum and spectral theory | 55P50 | Geometry | 15B52 | 81T13 | Supersymmetric gauge theories | Topological string | 57R56 | Matrix models | 81T60 | Group Theory and Generalizations | 81Q10 | 51P05 | 81Q80 | 81Q60 | Fermi gas, Matrix models | PAINLEVE-III | TOPOLOGICAL STRINGS | RANDOM LATTICE | DUALITY | MATRIX MODELS | PHYSICS, MATHEMATICAL | O(N) MODEL

70S15 | Fermi gas | 82D05 | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Quantum and spectral theory | 55P50 | Geometry | 15B52 | 81T13 | Supersymmetric gauge theories | Topological string | 57R56 | Matrix models | 81T60 | Group Theory and Generalizations | 81Q10 | 51P05 | 81Q80 | 81Q60 | Fermi gas, Matrix models | PAINLEVE-III | TOPOLOGICAL STRINGS | RANDOM LATTICE | DUALITY | MATRIX MODELS | PHYSICS, MATHEMATICAL | O(N) MODEL

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 1/2015, Volume 105, Issue 1, pp. 109 - 148

3d $${\mathcal{N}=2}$$ N = 2 partition functions on the squashed three-sphere $${S^{3}_{b}}$$ S b 3 and on the twisted product $${S^{2} \times S^{1}}$$ S 2 × S...

localization | supersymmetry | Theoretical, Mathematical and Computational Physics | deformed Virasoro algebra | conformal field theory | Statistical Physics, Dynamical Systems and Complexity | Physics | Geometry | 17B68 | 81R10 | 81T20 | gauge theory | 81T60 | Group Theory and Generalizations | 81T40 | VIRASORO ALGEBRA | PHYSICS, MATHEMATICAL | LIOUVILLE THEORY | Algebra | Physics - High Energy Physics - Theory

localization | supersymmetry | Theoretical, Mathematical and Computational Physics | deformed Virasoro algebra | conformal field theory | Statistical Physics, Dynamical Systems and Complexity | Physics | Geometry | 17B68 | 81R10 | 81T20 | gauge theory | 81T60 | Group Theory and Generalizations | 81T40 | VIRASORO ALGEBRA | PHYSICS, MATHEMATICAL | LIOUVILLE THEORY | Algebra | Physics - High Energy Physics - Theory

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 9/2019, Volume 109, Issue 9, pp. 1961 - 2001

We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of...

Topological string theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Supersymmetric gauge theory | Painlevé equations | 34M55 | Physics | Geometry | 15B52 | 81T13 | Spectral theory | 14H70 | 81T60 | Group Theory and Generalizations | 51P05 | 81Q10 | Painleve equations | INTEGRABLE MAPPINGS | TOPOLOGICAL STRINGS | SYMMETRY | DUALITY | SYSTEMS | MATRIX MODELS | PHYSICS, MATHEMATICAL | OPERATORS | String theory | Resveratrol

Topological string theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Supersymmetric gauge theory | Painlevé equations | 34M55 | Physics | Geometry | 15B52 | 81T13 | Spectral theory | 14H70 | 81T60 | Group Theory and Generalizations | 51P05 | 81Q10 | Painleve equations | INTEGRABLE MAPPINGS | TOPOLOGICAL STRINGS | SYMMETRY | DUALITY | SYSTEMS | MATRIX MODELS | PHYSICS, MATHEMATICAL | OPERATORS | String theory | Resveratrol

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 5/2014, Volume 104, Issue 5, pp. 585 - 612

Original proofs of the AGT relations with the help of the Hubbard–Stratanovich duality of the modified Dotsenko–Fateev matrix model did not work for β ≠ 1,...

Geometry | Theoretical, Mathematical and Computational Physics | generalized Jack polynomials | 05E05 | 81T60 | conformal field theory | AGT-conjecture | Group Theory and Generalizations | 81T40 | Statistical Physics, Dynamical Systems and Complexity | Physics | Conformal field theory | Generalized Jack polynomials | HILBERT SCHEMES | YANG-MILLS | ALGEBRA | QUIVER VARIETIES | MONOPOLES | PHYSICS, MATHEMATICAL | COHOMOLOGY | PRODUCT | EXPANSION | DUALITY | CONFORMAL BLOCKS | Analysis | Algebra

Geometry | Theoretical, Mathematical and Computational Physics | generalized Jack polynomials | 05E05 | 81T60 | conformal field theory | AGT-conjecture | Group Theory and Generalizations | 81T40 | Statistical Physics, Dynamical Systems and Complexity | Physics | Conformal field theory | Generalized Jack polynomials | HILBERT SCHEMES | YANG-MILLS | ALGEBRA | QUIVER VARIETIES | MONOPOLES | PHYSICS, MATHEMATICAL | COHOMOLOGY | PRODUCT | EXPANSION | DUALITY | CONFORMAL BLOCKS | Analysis | Algebra

Journal Article